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Construction and approximation of surfaces by discrete PDE splines on a polygonal domain

Authors
Journal
Applied Numerical Mathematics
0168-9274
Publisher
Elsevier
Publication Date
Volume
59
Issue
1
Identifiers
DOI: 10.1016/j.apnum.2008.02.001
Keywords
  • Approximation
  • Interpolation
  • Splines
  • Surfaces
  • Finite Elements
  • Pde

Abstract

Abstract This paper deals with the construction and characterization of discrete PDE splines on a polygonal domain. For this purpose, we need a PDE equation (usually an elliptic PDE), certain boundary conditions and a set of points to approximate. We thus demonstrate the convergence of a discrete PDE spline to a function of a fixed space in two different cases: (1) when the approximation points are fixed; (2) when the boundary points are fixed. To illustrate, we provide several numerical and graphic examples of construction and approximation by discrete PDE splines.

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